The task of finding such a \(z \in \mathcal {C}\)  boils down to finding a
solution \(\tilde{z} \in \mathbb {F}_2^n\)  to a \(\textsf {MAX t-XOR} \)  instance, up
to a an additive loss of \(O(\delta )\)  in the fraction of constraints
satisfied by the optimal solution. While this is hard to do in
general [1]}, [2]}, [3]} (building
on [4]}) show that this can be done if the instance satisfies
a special property called
splittability.
To define this, we let \(W[t_1,t_2] \subset [n]^{t_2-t_1+1}\)  denote the
collection of \((t_2-t_1+1)\) -tuples obtained by considering the indices
between \(t_1\)  and \(t_2\)  for all tuples in \(W(t)\) . We also assume that all
\(w \in W[t_1,t_2]\)  can be extended to the same number of tuples in \(W(t)\) 
(which is true for walks).
